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## Statistics and probability

### Unit 12: Lesson 4

Tests about a population mean- Writing hypotheses for a significance test about a mean
- Writing hypotheses for a test about a mean
- Conditions for a t test about a mean
- Reference: Conditions for inference on a mean
- Conditions for a t test about a mean
- When to use z or t statistics in significance tests
- Example calculating t statistic for a test about a mean
- Calculating the test statistic in a t test for a mean
- Using TI calculator for P-value from t statistic
- Using a table to estimate P-value from t statistic
- Calculating the P-value in a t test for a mean
- Comparing P-value from t statistic to significance level
- Making conclusions in a t test for a mean
- Free response example: Significance test for a mean

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# Comparing P-value from t statistic to significance level

AP.STATS:

DAT‑3 (EU)

, DAT‑3.E (LO)

, DAT‑3.E.1 (EK)

, DAT‑3.F (LO)

, DAT‑3.F.1 (EK)

, DAT‑3.F.2 (EK)

Example showing how to compare the P-value to a significance level to make a conclusion in a t test.

## Want to join the conversation?

- Shouldn't we divide alpha by 2, since the test is considering a two-tailed hypothesis?(6 votes)
- It seems that the p-value given took all of that into consideration already. As all calculations were given.(3 votes)

- this is a two tailed test, isn't P-value doubled ? i think he got it wrong(2 votes)
- He already did that prior to the final calculation.(2 votes)

- Isn't this type of "strong" conclusion why polls are always wrong?(2 votes)
- Above error is present.

Square root should be 19.

To get the correct answer you have to take the square root of 20(1 vote) - how much drink was in the drinks per drinks...(0 votes)

## Video transcript

- [Instructor] Jude was curious
if the automated machine at his restaurant was filling
drinks with the proper amount. He filled a sample of 20 drinks
to test his null hypothesis, which is the actual population mean for how much drink
there was in the drinks, per drink is 530 milliliters, versus his alternative hypothesis is that the population mean
is not 530 milliliters, where mu is the mean filling amount. The drinks in the sample contained a mean amount of 528 milliliters with a standard deviation
of four milliliters. These results produced a test statistic of t is equal to negative 2.236 and a P-value of approximately 0.038. Assuming the conditions
for inference were met, what is an appropriate conclusion at the alpha equals 0.05 significance level? And they give us some choices here. And like always, I encourage
you to pause this video and see if you can figure
it out on your own. All right, so now let's
work through this together. So let's just remind
ourselves what's going on. So you have some population of drinks, and we care about the
true population mean. You have a null hypothesis around it, that the true mean is 530 milliliters, but then there's the
alternative hypothesis that it's not 530 milliliters. So to test your null
hypothesis, you take a sample. In this case, we had
a sample of 20 drinks. And using that sample, you
calculate a sample mean, and then you also calculate
a sample standard deviation. They tell us these things right over here. And then using this information and actually our sample size, you are able to calculate a t-statistic. You're able to calculate a t-statistic. And then using that t-statistic, you are able to calculate a P-value. And the P-value is what is the probability of getting a result at least this extreme if we assume that the
null hypothesis is true? And if that probability is lower than our significance level, then we say, hey, that's
a very low probability. We are going to reject
our null hypothesis, which would suggest our alternative. So the key to this
question is just to compare this P-value right over here
to our significance level. And as we see, the P-value 0.038 is indeed less than 0.05. And so, because of this, we would reject the null hypothesis. We would reject the null hypothesis, which would suggest the alternative, that the true mean is something different
than 530 milliliters. And so if we look our choices here, so the first choice says
reject the null hypothesis. This is strong evidence
that the mean filling amount is different than 530 milliliters. Yeah, that one looks good. This suggests this is strong evidence, this suggests the alternative hypothesis, which is that right over there. But let's read the other
ones just to make sure that they don't make sense. So this is rejecting the null hypothesis. That looks true so far. This isn't enough evidence to conclude that the mean filling amount is different than 530 milliliters. No, not, the first one is
definitely much stronger. Fail to reject the null hypothesis. No, we are rejecting the null hypothesis 'cause our P-value is lower
than our significance level. Fail to reject, no we'd
rule that one out as well.